V. Reinhart wrote on Sat, Jul 22, 2017 07:57 PM UTC:
HGMuller's formula is interesting, and it's good to see there's a way to expand its scope by using ELC. Muller presented the formula as:
value = 33*ELC + (33*ELC)*(33*ELC)/1584)
I prefer it a little more as:
value = 33*ELC + 0.6875*(ELC)^2
In this form the variable occurs once for its linear component (33xELC) and once for its polynomial component (0.6875*(ELC)^2).
But this is just a minor stylistic preference. More generally, it's very interesting that a rather simple formula can be quite accurate for a wide range of leapers. Not sure if there's any future possibility (by Muller or others) to ammend it for longer range leapers. Of course, work like this always requires a lot of engine analysis, and follow-up evaluation of the data.
Good work on the formula!
Btw, do we know that Lasker's estimate of a king's value in an endgame (4) might not be too far off? The study that I did (which basically just confirmed previous work by Muller) was to estimate the value of a guard/commoner for the entirety of a chess-game (10x8 board).
From my study alone, I cannot dispute Lasker's estimate. As far as I know, it might be possible that a non-royal king might be worth a little more on an 8x8 board, and yet a little more in an end-game only situation.
HGMuller's formula is interesting, and it's good to see there's a way to expand its scope by using ELC. Muller presented the formula as:
value = 33*ELC + (33*ELC)*(33*ELC)/1584)
I prefer it a little more as:
value = 33*ELC + 0.6875*(ELC)^2
In this form the variable occurs once for its linear component (33xELC) and once for its polynomial component (0.6875*(ELC)^2).
But this is just a minor stylistic preference. More generally, it's very interesting that a rather simple formula can be quite accurate for a wide range of leapers. Not sure if there's any future possibility (by Muller or others) to ammend it for longer range leapers. Of course, work like this always requires a lot of engine analysis, and follow-up evaluation of the data.
Good work on the formula!
Btw, do we know that Lasker's estimate of a king's value in an endgame (4) might not be too far off? The study that I did (which basically just confirmed previous work by Muller) was to estimate the value of a guard/commoner for the entirety of a chess-game (10x8 board).
From my study alone, I cannot dispute Lasker's estimate. As far as I know, it might be possible that a non-royal king might be worth a little more on an 8x8 board, and yet a little more in an end-game only situation.